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Bunuel
There is at least one viper and at least one cobra in Pandora's box. How many cobras are there?

(1) From any two snakes from Pandora's box at least one is a viper.
(2) The total number of snakes in Pandora's box is 99.

Given: There is at least one viper and at least one cobra in Pandora's box.

Target question: How many cobras are there?

Statement 1: From any two snakes from Pandora's box at least one is a viper.
This tells us that there CANNOT be more than one cobra in the box.
For example, if there were TWO cobras and the box, then it's possible to have two snakes (both cobras) such that neither is a viper, which would break the condition that at least one snake must be a viper.
Since we are told there is at least one cobra, and since we have now concluded that there CANNOT be more than one cobra in the box, the answer to the target question is there is exactly 1 cobra in the box
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The total number of snakes in Pandora's box is 99
There are many scenarios that satisfy statement 2. Here are two:
Case a: There are 10 cobras and 89 vipers. In this case, the answer to the target question is there are 10 cobras in the box
Case b: There are 11 cobras and 88 vipers. In this case, the answer to the target question is there are 11 cobras in the box
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation. Great question, really caught me off guard.
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This has to be one of the best probability questions on gmatclub!
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I think this is a high-quality question and I agree with explanation.
yes agred!
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Never thought that I could ever be in LOVE with a GMAT question! :D
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I think this is a very easy question if you think mathematically. In the probability formula if you are picking two random snakes and given that out of the two picks at least one will be a viper means that in one of the pick the probability of picking Viper is 1 cause the stem tells us that there's going to be at least one cobra. In that case when you are picking 2, first one you pick will be either a cobra or a viper. If the first one is a cobra, then second must be a viper (Probability =1), given in any two picks at least one is a viper, this indirectly tells you that there's 1 Cobra in the box!

Love this logic and the question Bunuel!
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation. Really good question. This is the first time I've come across such type of question.
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Bunuel
There is at least one viper and at least one cobra in Pandora's box. How many cobras are there?


(1) From any two snakes from Pandora's box at least one is a viper.

(2) The total number of snakes in Pandora's box is 99.

Responding to a pm:

(1) From any two snakes from Pandora's box at least one is a viper.

What does this mean? It means that if you pick any two snakes from the box, at least one of them is certainly a viper. So it is not possible for you to pick 2 snakes which are both non-viper. It means that there is at most 1 non-viper snake.
Since we are given that there is at least one cobra, it means the one non-viper snake must be a cobra.
So of the total snakes in the box, exactly 1 is cobra and all others are viper.

Think what happens if there are 2 non-viper snakes in the box. Then if you pick 2 snakes, there is a chance that both are not viper (if you pick the two non-vipers). But we have been given that whenever you pick 2 snakes, one will ALWAYS be a viper.
Hence there aren't 2 non-viper snakes.

This statement is sufficient to tell us that there is just 1 cobra.

Statement 2 alone doesn't help us figure how many cobras there are.

Answer (A)
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Such a lovely question to get right in first attempt, that too within time limit.

If there is 1 out of 2 Viper. So no matter how many snakes (x) there will be always (x-1) Vipers to make this case true.

favourable/ Total. At least 1 or both. It’s the other way round we need to find a way that can prove the statement wrong and eliminate that possibility, what if there are 2 cobras and 28 Vipers. We will def have 1 case of 2 Cobras being picked. but that contradicts the question so we confirm x-1 vipers. now because there is at least 1 cobra that 1 in x-1 is the 1 cobra
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Bunuel
There is at least one viper and at least one cobra in Pandora's box. How many cobras are there?


(1) From any two snakes from Pandora's box at least one is a viper.

(2) The total number of snakes in Pandora's box is 99.
This one is tricky.

Given: Box has at least 1 cobra and at least 1 viper.
Q: no of cobras?

1) From any two snakes chosen at random at least one is a viper, which means that there is only one cobra in the box.
because 2 or more no cobras are there then at random two cobras can be picked, which is contradictory to given statement.

Hence there is only 1 cobra. Sufficient

2)Total snakes =99. we don't have any info about no of vipers and cobras. this can be 98 vipers+ 1 cobra or 1 viper+ 98 cobras.
Hence insuffiecient.

Ans: A
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I like the solution - it’s helpful.
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I like the solution - it’s helpful.
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